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19.102 (2018)

Open

A subgroup $H$ of a free group $F$ is called inert if $r(H \cap K) \leqslant r(K)$ for every $K \leqslant F$; and compressed if $r(H) \leqslant r(K)$ for every $H \leqslant K \leqslant F$. Is it true that compressed subgroups are inert?

Contributor: E. Ventura

Progress

*Yes, it is true (A. Jaikin-Zapirain, Preprint, 2024, https://arxiv.org/pdf/2403.09515).

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